That's four questions
1. I've always played it that they only Poison heroes on a called shot as per LMB p50 in the combat example . (Otherwise there would be stacks of companions sleeping away the combat.)
2. The fact that Poison (from a sting) is the Called Shot surely means that they can use it when a Hero has rolled an Eye even if they don't have the target Ensnared. If they Ensnare with any Tengwars they get a free sting or bite but can't Poison LMB p50 again.
3. Although I could never find it (except in the combat example p50 LMB )I think that from various phrasings the intent is that the first listed attack is the primary attack. There's nothing I remember that says an Adversary has to use it's primary attack, but sometimes the mechanisms make it obvious that one has to proceed before the other (i.e. Savage Assault).
Note however that Common Weapons LMB p65 says "This entry lists the characteristics of the weapons or
attack types commonly employed by the creatures."
Under the Common Weapons section for the Spiders it says "The Spiders of Mirkwood’s poison is their most formidable threat:"
4. Someone Ensnared cannot change Stance and their Parry is halved. If I remember correctly you may cut yourself free from webbing using the Dagger/Unarmed skill. This suggests to me that you cannot otherwise use a weapon while Ensnared.
